Question: Solve for $z$, $ \dfrac{z - 7}{2z - 8} = \dfrac{1}{7} $
Multiply both sides of the equation by $2z - 8$ $ z - 7 = \dfrac{2z - 8}{7} $ Multiply both sides of the equation by $7$ $ 7(z - 7) = 2z - 8 $ $7z - 49 = 2z - 8$ $5z - 49 = -8$ $5z = 41$ $z = \dfrac{41}{5}$